Minimum Manhattan Distance Approach to Multiple Criteria Decision Making in Multiobjective Optimization Problems

Chiu, Wei‐Yu; Yen, Gary G.; Juan, Teng-Kuei

doi:10.1109/tevc.2016.2564158

Cited by 113 publications

(40 citation statements)

References 42 publications

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“…Hence, in the absence of any preferences, the knee-point structures can be considered for further analysis. To this end, Minimum Manhattan Distance (MMD) approach has been selected, which is similar to Divide & Conquer approach to identify the knee-point solution, albeit MMD is computationally more efficient [67].…”

Section: Minimum Manhattan Distancementioning

confidence: 99%

Multi-objective evolutionary framework for non-linear system identification: A comprehensive investigation

2020

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The present study proposes a multi-objective framework for structure selection of nonlinear systems which are represented by polynomial NARX models. This framework integrates the key components of Multi-Criteria Decision Making (MCDM) which include preference handling, Multi-Objective Evolutionary Algorithms (MOEAs) and a posteriori selection. To this end, three well-known MOEAs such as NSGA-II, SPEA-II and MOEA/D are thoroughly investigated to determine if there exists any significant difference in their search performance. The sensitivity of all these MOEAs to various qualitative and quantitative parameters, such as the choice of recombination mechanism, crossover and mutation probabilities, is also studied. These issues are critically analyzed considering seven discretetime and a continuous-time benchmark nonlinear system as well as a practical case study of non-linear wave-force modeling. The results of this investigation demonstrate that MOEAs can be tailored to determine the correct structure of nonlinear systems. Further, it has been established through frequency domain analysis that it is possible to identify multiple valid discrete-time models for continuous-time systems. A rigorous statistical analysis of MOEAs via performance sweet spots in the parameter space convincingly demonstrates that these algorithms are robust over a wide range of control parameters.of correct terms which captures the system dynamics is one of the major challenges of the system identification [6,7], and, therefore, is the main focus of this investigation.The exhaustive search to solve the structure selection problem is intractable even for moderate number of terms 'n', as this would require an evaluation of 2 n term subsets/structures. The structure selection problem is often 'NP-Hard' [13] and therefore requires an efficient search strategy. Since the search for system structure is primarily dependent on the limited number of observed data, it involves bias-variance trade-off [2, 3, 7], i.e., too sparse a structure may yield a high bias error (under-fitting) whereas a very complex structure may yield a high variance error (over-fitting). Further, earlier investigations [14,15] show that the over-fitted structures tend to induce 'ghost' dynamics which are not present in the actual system. Pursuing these arguments, it is clear that determination of the size of the identified structure (i.e., number of terms or 'cardinality') is a critical aspect of the structure selection process. However, this issue has received relatively less attention in the existing investigations.Among the existing structure selection approaches, the Orthogonal Forward Regression (OFR) proposed by Billings and Korenberg [16] has extensively been studied. It is a sequential model building approach in which the most significant term is added in each step, which is determined on the basis of a statistical criterion. Over the years, this notion of the original OFR approach has been refined to further improve the search performance. These include OFR approaches...

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Section: Minimum Manhattan Distancementioning

confidence: 99%

Multi-objective evolutionary framework for non-linear system identification: A comprehensive investigation

2020

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“…In practice, the knee of the approximate Pareto front is often preferred for several reasons: it can achieve excellent overall system performance if the front is bent; it represents the solution closest to the ideal one that is not reachable; and it has rich geometrical and physical meanings [85], [86]. In Step 3, the knee solution is selected according to [87]:…”

Section: End Whilementioning

confidence: 99%

Pareto Optimal Demand Response Based on Energy Costs and Load Factor in Smart Grid

Chiu

Hsieh

Chen

2020

IEEE Trans. Ind. Inf.

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Demand response for residential users is essential to the realization of modern smart grids. This paper proposes a multiobjective approach to designing a demand response program that considers the energy costs of residential users and the load factor of the underlying grid. A multiobjective optimization problem (MOP) is formulated and Pareto optimality is adopted. Stochastic search methods of generating feasible values for decision variables are proposed. Theoretical analysis is performed to show that the proposed methods can effectively generate and preserve feasible points during the solution process, which comparable methods can hardly achieve. A multiobjective evolutionary algorithm is developed to solve the MOP, producing a Pareto optimal demand response (PODR) program. Simulations reveal that the proposed method outperforms the comparable methods in terms of energy costs while producing a satisfying load factor. The proposed PODR program is able to systematically balance the needs of the grid and residential users.

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“…An exhaustive search of all possible term subsets to solve (19) is often intractable even for a moderate number of NARX terms 'n', as it requires the examination of 2 n term subsets/structures. Hence, it is clear that an effective search strategy is crucial to optimize the multi-objective structure selection problem given by (19). This can be accomplished by any multi-objective evolutionary algorithm such as NSGA-II [15], SPEA-II [16], MOEA/D [17] and others.…”

Section: B Multi-objective Structure Selectionmentioning

confidence: 99%

“…The comparative analysis of these algorithms on the structure selection problem in [18] indicates that NSGA-II often yields an improved Pareto front in comparison to SPEA-II and MOEA/D. Hence, in this study, NSGA-II is selected to solve the structure selection problem given in (19).…”

Section: B Multi-objective Structure Selectionmentioning

confidence: 99%

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MultiObjective Evolutionary Approach to Grey-Box Identification of Buck Converter

Hafiz

Swain

Mendes

et al. 2020

IEEE Trans. Circuits Syst. I

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The present study proposes a simple grey-box identification approach to model a real dc-dc buck converter operating in continuous mode using a nonlinear polynomial autoregressive with exogenous input (NARX) model. The proposed approach casts the grey-box identification problem into a multi-objective framework and explicitly uses a priori information about the static nonlinearity into the structure selection process. The multiobjective framework could identify globally valid models with improved dynamic prediction and can mimic the static behavior of the buck converter over a wide input range.

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Minimum Manhattan Distance Approach to Multiple Criteria Decision Making in Multiobjective Optimization Problems

Cited by 113 publications

References 42 publications

Multi-objective evolutionary framework for non-linear system identification: A comprehensive investigation

Multi-objective evolutionary framework for non-linear system identification: A comprehensive investigation

Pareto Optimal Demand Response Based on Energy Costs and Load Factor in Smart Grid

MultiObjective Evolutionary Approach to Grey-Box Identification of Buck Converter

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